Joe, help us a bit with more info. When you say "high" do you mean the high range on the transmission or the "rabbit" position of the rabbit-turtle switches? If you mean the "rabbit" position, it could be that your solenoid that engages to give you rabbit is overheating. Is the burning smell electrical smelling or like oil?
With just a little more info, we'll be able to help you a lot better.
Welcome to TBN. I think you will find that almost all tractor problems can be diagnosed on this site, but more information is needed with regards to your experience with Hydrostatic transmissions and tractors and the conditions that cause the problem: trying to start in Range II-"Rabbit" on level ground? going up a hill? pulling a plow? When it stops is it because you stop on purpose and smell the unusual smell? or the enging lugs down and stalls itself? Does the engine run smoothly, from 750 up to 2700 RPM while in neutral? Starting in Range I-"Turtle", move the tractor forward at 2600 RPM, will the tractor move smoothly. While at top speed while doing this, push the "Rabbit" button. Is there an immediately noticed increase in tractor speed? Will Range II-"Turtle" work the properly over the same RPM range?
If you are not experienced with Hydrostatic Transmissions, I suspect you are are running at too low RPMs and are using the HST pedal like an accelerator. It is really an infinitely adjustable torque adjuster. It you want maximimum torque at the wheels, you must be in the lowest gear range, RPM at ~2600, and the slightest pressure on the pedal - you will move slowly, but you'll be amazed at how much torque you can get. It is not good for diesel engines to be bogged down so much that they stall.
Yes, to go along with what Chris said, constantly keeping your HST transmission in a stall mode will open the relief pressure valve inside the transmission and cause the oil to heat up. That relief valve opens at 5000 psi. That's a lot of pressure. If you don't smell the smell in low/rabbit, then it is not the rabbit solenoid. I think you are just heating up the hydraulic oil and you are smelling that.